The suspension system of a vehicle has two principle functions, first to isolate the vehicle body and consequently the vehicle's passengers from road inputs, and second to improve the vehicle's road holding by reducing the load variation between the wheels of the vehicle and the ground.
The behaviour of a vehicle's suspension system can be characterised in terms of the suspension system's vertical and longitudinal compliance.
The vertical compliance of vehicle suspension systems is typically created by spring-damper systems that are tuned to provide a good compromise between passenger comfort and handling performance. The springs are chosen to have a resonant frequency of the sprung mass between about 0.7 Hz and 2 Hz. Lower resonant frequencies induce travel sickness whereas higher frequencies reduce the suppression of road inputs. Stiff damping results in a harsh ride but soft damping results in long lasting car body motion following disturbance and large load variation between wheel and road.
In contrast, to maintain good wheel control the longitudinal compliance of a vehicle is generally significantly stiffer than that of the vertical compliance; otherwise the torque provided by the brake or drive-train acts on the vehicle body through a soft suspension system, thereby reducing the driver's ability to maintain vehicle control. As a consequence the longitudinal compliance of a vehicle's suspension system is typically provided primarily by bushings.
As with the vertical compliance of a suspension system, there is also a compromise with respect to the longitudinal compliance between passenger comfort, which is increased by softening the damping, and the need to dampen oscillations in the cabin to maintain good vehicle control.
For example, a road surface disturbance such as a pot-hole induces a longitudinal force impulse on a vehicle's wheel, where the longitudinal force causes an initial shock that is felt by the occupants of the vehicle followed by a vibration. Increasing the longitudinal stiffness increases the initial shock but reduces the duration of the subsequent vibration for a given road disturbance.
The longitudinal behaviour of a suspension system can be illustrated with the simplified quarter-car two degree-of-freedom model shown in FIG. 1. mu represents the unsprung mass, for example a wheel and associated parts, and ms represents the sprung mass, the quarter-car body. The longitudinal compliance of the suspension is represented by the spring-damper system with spring constant k and damping constant b. The positions of the unsprung and sprung mass in the longitudinal direction are shown as xu and xs respectively. The longitudinal component of the force imparted by the road surface on the unsprung mass is shown as Fr(t).
The motion of the sprung mass in response to an imperfect road surface generally determines the comfort of the vehicles passengers. The key features of motion associated with passenger discomfort are the magnitude and duration of the rate of change of acceleration, otherwise known as vehicle jerk, resulting from road surface imperfections.
In response to a shock, such as that caused by a wheel of a vehicle hitting a pot-hole in a road surface, there is an initial high magnitude jerk followed by oscillations. Both of these features can be unpleasant to a passenger of a vehicle. However, whereas the optimum means for minimising the initial jerk requires weak damping, in contrast the optimum means for minimising the subsequent oscillations requires strong damping.
FIG. 2 illustrates the conflict between the requirements for strong and weak damping with respect to longitudinal compliance for a passive suspension system, where the left hand plot 20 in FIG. 2 reflects rate of change of acceleration versus time for a strong damping system and the right hand plot 22 in FIG. 2 reflects rate of change of acceleration versus time for a weak damping system. For the purposes of the plots illustrated in FIG. 2, the plots are based on the simplified quarter car two degree of freedom model illustrated in FIG. 1 using the following parameters: mu=50 kg, ms=400 kg, k=444 N/mm. For the strong damping plots b=1.5 Ns/mm and for the weak damping plots b=0.3 Ns/mm. Both masses are initially moving at 15 m/s and a pot-hole strike is simulated by constructing Fr(t) as a half sinusoid of duration 5 ms and amplitude 10000 N. This imparts an initial acceleration of about 200 m/s/s to the unsprung mass, i.e. the wheel. The plots illustrated in FIG. 2 show the resulting jerk as a function of time of the sprung mass, i.e. the vehicle body.
The upper plots illustrated in FIG. 2 show that the weak damped system leads to a long-lasting longitudinal oscillation of the vehicle body whereas the strong damped system quickly suppresses oscillations after the initial impact. The lower plots show the same data on an expanded time-scale to show the rate of change of acceleration of the vehicle body shortly after the impact time. The maximum magnitude of the jerk in the strongly damped case is about 1100 m/s/s/s whereas it is about 700 m/s/s/s in the weakly damped case. This figure represents the initial shock felt by the occupants of the vehicle.